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41.

The prime numbers which are less than 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23.

  1. 2 + 23 Using two numbers
  2. 3 + 3 + 19 Using three numbers
  3. 3 + 5 + 17
  4. 3 + 11 + 11
  5. 5 + 7 + 13
  6. 7 + 7 + 11
  7. 2 + 2 + 2 + 19 Using four numbers
  8. 2 + 3 + 3 + 17
  9. 2 + 3 + 7 + 13
  10. 2 + 5 + 5 + 13
  11. 2 + 5 + 7 + 11
  12. 2 + 2 + 2 + 2 + 17 Using five numbers
  13. 2 + 2 + 3 + 5 + 13
  14. 2 + 2 + 3 + 7 + 11
  15. 2 + 2 + 5 + 5 + 11
  16. 2 + 2 + 7 + 7 + 7
  17. 3 + 3 + 3 + 3 + 13
  18. 3 + 3 + 3 + 5 + 11
  19. 3 + 3 + 5 + 7 + 7
  20. 3 + 5 + 5 + 5 + 7
  21. 5 + 5 + 5 + 5 + 5
  22. 2 + 2 + 2 + 3 + 3 + 13 Using six numbers
  23. 2 + 2 + 2 + 3 + 5 + 11
  24. 2 + 2 + 2 + 5 + 7 + 7
  25. 2 + 3 + 3 + 3 + 3 + 11
  26. 2 + 3 + 3 + 3 + 7 + 7
  27. 2 + 3 + 3 + 5 + 5 + 7
  28. 2 + 3 + 5 + 5 + 5 + 5
  29. 3 + 3 + 3 + 3 + 3 + 5 + 5 Using seven numbers
  30. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 11 Using eight numbers
  31. 2 + 2 + 2 + 3 + 3 + 3 + 3 + 7
  32. 2 + 3 + 3 + 3 + 3 + 3 + 3 + 5
  33. 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 7 Using nine numbers
  34. 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 5
  35. 2 + 2 + 3 + 3 + 3 + 3 + 3 + 3 + 3
  36. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 7 Using ten numbers
  37. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 5
  38. 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3
  39. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 5 Using eleven numbers
  40. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3
  41. 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 Using twelve numbers
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Q: How many ways can you make 25 with only prime numbers?
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